Some private schools are refusing to set up academies because they fear they could be a fad that will be reversed by the next government, the former head of Harrow School has warned.

Barnaby Lenon, now chairman of the Independent Schools Council, said some headteachers also fear they will lose pupils if they set up a high-quality state school in their catchment area.

Education Secretary Michael Gove has urged private schools to support the academies and free school programme. David Cameron even hosted a Downing Street reception for private-school heads to encourage them to set up state schools which are independent of council control but do not charge fees.

While some leading independent institutions, including Eton and Wellington College, have embraced the idea, Mr Lenon admitted not all have “leaped into setting up free schools and academies”. Speaking at a Spectator education conference, he said: “There is a fear among schools that academies and free schools are in favour politically at the moment, but might be superseded by a new policy in due course.”

He added that headteachers had seen many changes in the past 20 years, including a shift away from assisted places and independent state school partnerships. Referring to setting up academies he said: “Policy changes of this sort leave some schools somewhat reluctant to commit to something that might be rather transitory.”

Lord Adonis, an architect of Labour’s academies programme, dismissed the remarks, saying: “No sane government is going to want to take on a body of parents who have a successful school to which they send their children.”

Toby Young, who co-founded West London Free School, called on shadow education secretary Stephen Twigg to confirm a Labour government would not interfere with free schools and ac-ademies. But he added: “The best protection independent schools can create for themselves is becoming more em-bedded in the public sector: the harder it will be to attack them politically.”

During Mr Lenon’s time as head of Harrow, its charity donated £1 million to help set up the Chelsea Academy, of which he is still a governor. He also chairs the London Academy of Excellence, a free school in Newham run by eight private institutions including Brighton College, Eton, City of London School and Roedean.